I have frogs yearly in my dams where the cattle drink . They are in my flower beds , an i let them live there. I dont know if they die or not, but sure see them an hear them yearly. Today they were under my mums. I have a birdbath an mums all around it .Huge froggie was hiding under that. I dont kill them. The are insect eaters. b ps we are zone 5, an had 4 ft of snow last winter. Still have frogs out there. they bury themselves in the mud for the winter.
I tried the pan of mud idea and it didn't; work here in central Indiana. I would find dead frogs in my pond every spring right after thaw. I tried heaters and floating a light too. My pond would freeze deeper than the opening of the skimmer and the water would stop circulating. I built a stream in another area and left it run all winter The beginning of the stream is only a couple inches and the lower end is 3 feet deep. I remove some floating leaves and clean the skimmer in the fall but I leave a layer of leaves on the bottom that I net out in the spring. The water runs underneath the snow and ice all winter and the frogs survived. I think with my first pond the pump was not strong enough to keep the ice from damming at the skimmer.This winter I will take the pump out of the skimmer and set it in the larger pond area to keep the water moving but not have the waterfall.